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A geostatistical approach to estimate high resolution nocturnal bird migration densities from a weather radar network

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A geostatistical approach to estimate high resolution nocturnal bird migration densities from a weather radar network

Abstract and Figures

Quantifying nocturnal bird migration at high resolution is essential for (1) understanding the phenology of migration and its drivers, (2) identifying critical spatio-temporal protection zones for migratory birds, and (3) assessing the risk of collision with man-made structures. We propose a tailored geostatistical model to interpolate migration intensity monitored by a network of weather radars. The model is applied to data collected in autumn 2016 from 69 European weather radars. To cross-validate the model, we compared our results with independent measurements of two bird radars. Our model estimated bird densities at high resolution (0.2°latitude-longitude, 15min) and assessed the associated uncertainty. Within the area covered by the radar network, we estimated that around 120 million birds were simultaneously in flight [10-90 quantiles: 107-134]. Local estimations can be easily visualized and retrieved from a dedicated interactive website: birdmigrationmap.vogelwarte.ch . This proof-of-concept study demonstrates that a network of weather radar is able to quantify bird migration at high resolution and accuracy. The model presented has the ability to monitor population of migratory birds at scales ranging from regional to continental in space and daily to yearly in time. Near-real-time estimation should soon be possible with an update of the infrastructure and processing software.
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A geostatistical approach to estimate high resolution
nocturnal bird migration densities from a weather radar
network.
Rapha¨el Nussbaumer1,2,* , Lionel Benoit2, Gr´egoire Mariethoz2, Felix
Liechti1, Silke Bauer1& Baptiste Schmid1
1 Swiss Ornithological Institute, Sempach, Switzerland
2 Institute of Earth Surface Dynamics, University of Lausanne, Lausanne,
Switzerland
* raphael.nussbaume@vogelwarte.ch
Abstract
1. Quantifying nocturnal bird migration at high resolution is essential for (1)
understanding the phenology of migration and its drivers, (2) identifying critical
spatio-temporal protection zones for migratory birds, and (3) assessing the risk of
collision with man-made structures.
2. We propose a tailored geostatistical model to interpolate migration intensity
monitored by a network of weather radars. The model is applied to data collected
in autumn 2016 from 69 European weather radars. To cross-validate the model,
we compared our results with independent measurements of two bird radars.
3. Our model estimated bird densities at high resolution (0.2latitude-longitude,
15min) and assessed the associated uncertainty. Within the area covered by the
radar network, we estimated that around 120 million birds were simultaneously in
flight [10-90 quantiles: 107-134]. Local estimations can be easily visualized and
retrieved from a dedicated interactive website:
birdmigrationmap.vogelwarte.ch.
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4.
This proof-of-concept study demonstrates that a network of weather radar is able
to quantify bird migration at high resolution and accuracy. The model presented
has the ability to monitor population of migratory birds at scales ranging from
regional to continental in space and daily to yearly in time. Near-real-time
estimation should soon be possible with an update of the infrastructure and
processing software.
Keywords 1
Aeroecology, Bird migration, Geostatistical modelling, Interactive visualisation, Kriging,
2
Radar network, Spatio-temporal interpolation map, Weather radar. 3
Introduction 4
Every year, several billion birds undergo migratory journeys between their breeding and
5
non-breeding grounds (Dokter et al., 2018; Hahn, Bauer, & Liechti, 2009). These 6
migratory movements link ecosystems and biodiversity at a global scale (Bauer & Hoye,
7
2014), and their understanding and protection requires international efforts (Runge, 8
Martin, Possingham, Willis, & Fuller, 2014). Indeed, declines in many migratory bird 9
populations (Sanderson, Donald, Pain, Burfield, & van Bommel, 2006; Vickery et al., 10
2013) resulted from the rapid changes of their habitats, including the aerosphere (Diehl,
11
2013). Changes in aerial habitats are diverse, and their consequences still poorly 12
resolved. Nevertheless, climate change may alter global wind patterns and consequently
13
the wind assistance provided to migrants (La Sorte, Horton, Nilsson, & Dokter, 2019). 14
Likely more severe, the impact of direct anthropogenic changes include for instance light
15
pollution that reroute migrants (Van Doren et al., 2017), or buildings (Winger et al., 16
2019), wind energy production (Aschwanden et al., 2018), and aviation (van Gasteren et
17
al., 2019) that together cause billions of fatalities every year (Loss, Will, & Marra, 2015).
18
In the face of these threats and for setting up efficient management actions, we need
19
to quantify bird migration at various spatial and temporal scales. Fine scale monitoring
20
is crucial for understanding the phenology of migration and its drivers, identifying 21
critical spatio-temporal protection zones to enhance conservation actions, and assessing
22
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collision risks with human-made structures and aviation to inform stakeholders. 23
However, the great majority of migratory landbirds fly at night (Winkler, 1999), 24
challenging the quantification of the sheer scale of bird migration. 25
Radar monitoring has the potential to quantify migratory movements of birds at the
26
continental scale (Drake & Bruderer, 2017). Initially limited to single dedicated 27
short-range measurements, the use of existing weather radar networks provide 28
continuous monitoring over large geographical areas such as Europe or North America 29
(Gauthreaux, Belser, & van Blaricom, 2003; Shamoun-Baranes et al., 2014), and led to
30
an upswing of radar aeroecology (Bauer et al., 2017; Dokter et al., 2018; Van Doren & 31
Horton, 2018). One important challenge in using networks of weather radars is the 32
interpolation of their signals in space and time. Recent studies (Dokter et al., 2018; Van
33
Doren & Horton, 2018) have used relatively simple interpolation methods as they 34
targeted patterns at coarse spatial and/or temporal scales. However, these methods are
35
insufficient if higher spatial or temporal resolution is wanted such as for the 36
fundamental and applied challenges outlined above. 37
To achieve high resolution interpolation of migration intensity derived from weather
38
radars ( 20km-15min), we propose a tailored geostatistical framework able to model the
39
spatio-temporal pattern of bird migration. Starting from time series of bird densities 40
measured by a radar network, our geostatistical model produces a continuous map of 41
bird densities over time and space. A major strength of this method is its ability to 42
provide the full range of uncertainty and thus, to evaluate the probability that bird 43
densities reaches a given threshold. In addition to the estimation map, the method also
44
produces simulation maps which are essential for several applications such as 45
quantification of the total number of birds. 46
As a proof of concept, we applied our geostatistical model to a three weeks dataset 47
from the European Network of weather radar (Huuskonen, Saltikoff, & Holleman, 2014)
48
and validated the results with independent dedicated bird radar data. In addition to 49
insights into the spatio-temporal scales of broad front migration, our approach provides
50
high resolution (0.2
latitude and longitude, 15min) interactive maps of the densities of
51
migratory birds. 52
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Materials and Methods 53
Weather radar dataset 54
Our dataset originates from measurements of 69 European weather radars, spread from
55
Finland to the Pyrenees (8 countries) and covering the period from 19 September to 10
56
October 2016 (Figure 1). It thus encompasses a large part of the Western-European 57
flyway during fall migration 2016. 58
50°N
60°N
E
10°E
20°E
30°E
69
Temporal resolution
143km
(+/- 45km)
Distance to closest radar
Number of radars
Scanning distance
510 15
3
7
59
25km
S
64
5
40km
25km
Figure 1.
(Left) Locations of weather radars of the ENRAM network, whose fall 2016-data were used in this study
(yellow dots), and their key characteristics (right panel). We used data from two dedicated bird radars – in Switzerland
and France - for validation (red dots).
Based on the reflectivity measurements of these weather radars, we used the bird 59
densities as calculated and stored on the repository of the European Network for the 60
Radar surveillance of Animal Movement (ENRAM) 61
(github.com/enram/data-repository)(see (Nilsson et al., 2019) for details on the 62
conversion procedure). We inspected the vertical profiles and manually cleaned the bird
63
densities data (see detailed procedure in Supporting Information S1). 64
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Since we targeted a 2D model, we vertically integrated the cleaned bird densities 65
from the radar elevation and up to 5000 m above sea level. Because we aimed at 66
quantifying nocturnal migration, we restricted our data to night time, between local 67
dusk and dawn (civil twilight, sun 6below horizon). Furthermore, as rain might 68
contaminate and distort the bird densities calculated from radar data, a mask for rain 69
was created when the total column of rain water exceeds a threshold of 1mm/h (ERA5
70
dataset from (Copernicus Climate Change Service (C3S), 2017). In the end, the 71
resulting dataset consisted of a time series of nocturnal bird densities [bird/km
2
] at each
72
radar site with a resolution of 5 to 15 min (Figure 2). 73
Interpolation approach 74
Bird densities are strongly correlated both spatially at continental (Figure 2a-d) to 75
regional scales (Figure 2c), and temporally at daily (Figure 2b-d) to sub-nightly scales 76
(Figure 2e-g). 77
100
20
30
40
50 (a)
(b)
(c)
(d)
Sep 27 Sep 28
2016
Bird densities [bird/km2]
0
10
20
0
50
100
50
10
Sep 22 Sep 25 Sep 28 Oct 01 Oct 04 Oct 07 Oct 10
2016
(e)
(f)
(g)
Date
0
100
200
0
100
200
Bird densities [bird/km2]
200
0
0
100
30
Figure 2.
Space-time variability of bird densities as measured by a radar network. (a) Average bird densities over the
whole study period (time series of radar with a coloured outer circle represented in the subsequent panels, respectively).
(b-d) Time series of bird densities measured at different locations (colour of the dots corresponds to the colour of the
outer circle in panel a). (e-g) Zoom on a two-days period.
These strong spatio-temporal correlations motivated the choice of using a 78
geostatistical framework to interpolate the punctual radar observations. In such 79
framework, bird densities are considered as a space-time random process that is fully 80
defined by its covariance matrix (e.g. Chil`es & Delfiner, 1999). To perform optimally, 81
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however, geostatistical interpolation requires bird densities to be stationary (i.e. mean, 82
variance and covariance) in both space and time (e.g. Chil`es & Delfiner, 1999) – an 83
assumption hardly ever satisfied for migratory events. Rather, there are two main and 84
obvious non-stationarities in our dataset: (1) migration is more intense in the south 85
than in the north of Europe (Figure 2a), and (2) migration is more intense in the 86
middle of the night than during twilight (Figure 2e-g). To account for these 87
non-stationarities, we develop a tailored geostatistical model that decomposes the 88
migration signal into four independent components. 89
Geostatistical model 90
The bird density Z(s, t) observed at location sand at time tis modelled by 91
Z(s, t)p=τ(s) + γ(s, t) + A(s, t) + R(s, t),(1)
where
p
is a power transformation,
τ
the continental trend,
c
is the curve describing the
92
nightly trend, Athe nightly amplitude, and Rthe residual term (Figure 3). A power 93
transformation is used on bird densities in order to transform the highly skewed 94
marginal distribution into a Gaussian distribution (Figure S3-1 in Supporting 95
Information S3). The trend and the curve are deterministic functions accounting for the
96
two non-stationarities, whereas the amplitude and the residuals are stationary random 97
processes modelling the spatio-temporal variability at nightly and sub-nightly scales 98
respectively. The four components of the model are detailed in the following 99
sub-sections. 100
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Sep 26, 12:00 Sep 27, 00:00 Sep 27, 12:00 Sep 28, 00:00 Sep 28, 12:00 Sep 29, 00:00 Sep 29, 12:00
2016
0
10
20
30
40
50
60
70
80
Bird densities [bird/km2]
Trend
Amplitude
Curve
Residual
-1 10
Normalized Night Time (NNT)
-1 10 -1 01
0
Date
Figure 3.
Illustration of the proposed mathematical model decomposition into trend, amplitude, curve and residual.
Note that the power transformation was not applied on this illustration.
Trend 101
The increasing bird densities southwards (Figure 2a) create a first non-stationary in the
102
dataset. Although this trend changes over the year, it can be considered constant over 103
the short study period. Therefore, we model the trend as a deterministic planar 104
function 105
τ(s= [slat, slon ]) = wlatslat +w0,(2)
where slat and slon are latitude and longitude of location s,wlat is the slope coefficient 106
in latitude and
w0
is the value of the trend at the origin. Because no longitudinal trend
107
is observed in the data (Figure 1a), only latitude is used to parametrize the trend 108
function (see Figure S3-2 in Supporting Information S3). It is worth noting that if 109
longer periods are considered, Eqn. 2 should be replaced by a more complex parametric
110
function in order to handle the emerging patterns of long term non-stationarity. 111
Curve 112
The second non-stationarity visible in the dataset is the nightly pattern (Figure 2e-g) 113
that results from the onset and sharp increase of migration activity after sunset, and its
114
slow decrease towards sunrise (e.g. Bruderer & Liechti, 1995). Similar to the trend, this
115
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pattern needs to be extracted from the original signal to avoid non-stationarity. This is
116
done using a curve template
c
for all nights and locations, defined as the polynomial of
117
degree 6 118
γ(s, t) =
i=6
X
i=0
aiNNT(s, t)i,(3)
where aiare the coefficients of the polynomial and NNT (Normalized Night Time) is 119
the standardized proxy of the progression of night defined as 120
NNT(s, t) = 2tt(s, t)t(s, t)
t(s, t)t(s, t),(4)
where t(s, t) and t(s, t) are the times of civil dusk and dawn respectively. NNT is 121
defined such that the local sunrise or sunset occur at NNT =1 and NNT = 1, 122
respectively. 123
Amplitude 124
After removing the non-stationarities with the trend and the curve, the amplitude A125
models the nocturnal bird densities at the daily scale as a stationary space-time random
126
process. Its value is therefore constant within a night at a given location but varies 127
between locations and between nights. It accounts for the correlation at the scale of 128
several hundred kilometers and several days (Figure 1). 129
Residual 130
The variation in bird densities not modeled by trend, curve and amplitude, is still 131
strongly correlated in space and time at the hourly scale (Figure 2e-g). 132
Model parameterization 133
The values of the model parameters are determined by fitting the model to the observed
134
bird densities. In the Supporting Information S3, the parametrisation procedure is 135
detailed and the significance of the resulting parameters of the model are discussed. 136
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Bird migration mapping 137
After parametrisation, the geostatistical model can be used to interpolate bird density 138
observations derived from weather radars to produce high resolution maps. The full 139
mathematical description of the procedure is detailed in Supporting Information S2 and
140
a brief outline is given below. 141
The estimation of the bird density at any unsampled location
Z
(
s0, t0
)
is performed
142
by first estimating independently each component, and then recombining them 143
according to Eqn. 1. Estimating the deterministic components (i.e. trend and curve) is
144
straightforward since they can be computed by applying Eqn. 2 and 3 at the target 145
location and time s0, t0. Since the probabilistic components (amplitude and residual) 146
are modelled as random processes, the estimations of A(s0, t0)and R(s0, t0)are 147
performed by kriging (e.g. Chil`es & Delfiner, 1999; Goovaerts, 1997). An important 148
advantage of using kriging is that it expresses the estimation as a Gaussian distribution,
149
thus providing not only the “most likely value” (i.e. mean or expected value) but also a
150
measure of uncertainty with the variance of estimation. Tracking back the uncertainty 151
provided by kriging to the final estimation
Z
(
s0, t0
)
is non-trivial but possible through
152
the use of a quantile function (see Supporting Information S2 for details). Consequently,
153
the estimation
Z
(
s0, t0
)
is expressed as the median and its uncertainty range is defined
154
as the quantiles 10 and 90. A continuous space-time estimation (with uncertainty) map
155
is then computed by repeating the procedure for estimating a spatio-temporal point 156
s0, t0on a discrete set of points (i.e. grid). 157
In addition to the kriging estimation, we also provide simulation maps. Although 158
kriging is known to produce accurate point estimates, it leads to excessively smooth 159
interpolation maps (e.g. Goovaerts, 1997) and thus fails to reproduce the fine-scale 160
texture of the process at hand. Consequently, estimation should be complemented by 161
geostatistical simulation (e.g. Chil`es & Delfiner, 1999; Goovaerts, 1997) in applications
162
for which the space-time structure of the interpolation map matters (e.g. when 163
non-linear transformations are applied to the interpolated bird densities map, or when 164
aggregation in space or time is required). However, simulations come with a heavy 165
computational cost as a large ensemble of realisations is required to quantify the 166
uncertainty associated with the interpolation. 167
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In the case study presented in this paper, both estimation and simulations maps are
168
calculated on a spatio-temporal grid with a resolution of 0.2
in latitude (43
to 68
) and
169
longitude (-5to 30) and 15 minutes in time, resulting in 127x176x2017 nodes. Over 170
this large data cube, the estimation and simulation are only computed at the nodes 171
located (1) over land, (2) within 200km of the nearest radar and (3) during nighttime (
172
NNT(t, s)<1 or 1 < N N T (t, s)). 173
Validation 174
Cross validation 175
We tested the internal consistency of the model by cross-validation. It consists of 176
sequentially omitting the data of a single radar, then estimating bird densities at this 177
radar location with the model and finally, comparing the model-estimated value and 178
Z(s, t)observed data Z(s, t). The model is assessed by its ability to provide both the 179
smallest misfit errors, i.e. kZ(s, t)Z(s, t)k, and uncertainty ranges matching the 180
magnitude of these errors. Because it is difficult to quantify both aspects for a 181
non-normalized variable, the normalized error of estimation is used on the power 182
transformation variable 183
Z(s, t)Z(s, t)
σp
Z(s, t),(5)
where σp
Z(s, t) is the standard deviation of the estimation as defined in Eqn. S2-10 of 184
Supporting Information S2. 185
Comparison with dedicated bird radars 186
A second validation of our modelling framework (from data acquisition by weather 187
radars to geostatistical interpolation) is to compare model-predicted bird migration 188
intensities with the measurements of two dedicated bird radars (Swiss BirdRadar 189
Solution AG, swiss-birdradar.com) located in Herzeele, France (5053’05.6”N 190
2
32’40.9”E) and Sempach, Switzerland (47
07’41.0”N 8
11’32.5”E). These bird radars
191
register single echoes transiting through the radar beam, allowing to compute migration
192
traffic rates (MTR) and average speed of birds aloft (Nilsson et al., 2018; Schmid et al.,
193
2019). 194
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Results 195
Validation 196
Cross validation 197
In our study, the normalized error of estimation over all radars has a near-Gaussian 198
distribution with mean 0.017 and variance of 0.60 (Figure S4-1 in Supporting 199
Information S4). The near-zero mean of the error distribution indicates that our model
200
provides non-biased estimations of bird densities, while the near-one standard deviation
201
supports that the model provides appropriate uncertainty estimates, albeit slightly 202
overconfident. The performance of the cross-validation shows radar-specific biases (i.e. 203
constant under- or over-predictions)(Figure S4-2 in Supporting Information S4). The 204
biases are not spatially correlated (Figure S4-3 in Supporting Information S4) and 205
therefore such biases do not originate from the geostatistical model itself (or of 206
country-specific data quality). Rather, these radar-specific biases probably come from 207
either the data, such as birds non-accounted for (e.g. flying below the radar), or error in
208
the cleaning procedure (e.g. ground scattering). In contrast, the variances of the 209
normalized error of estimation of each radar are close to 1 and thus, demonstrate the 210
accuracy of the estimated uncertainty range (Figure S4-2 and Figure S4-3 in Supporting
211
Information S4). 212
Comparison with dedicated bird radars 213
The daily migration patterns estimated by our model coincide generally well with the 214
observations derived from dedicated bird radars (Figure 4). First, the estimations of the
215
model correctly reproduce the night-to-night migration intensity, with the exception of a
216
few nights (27-30 September for Herzeele and 26/27 September for Sempach). Second, 217
the intra-night fluctuations are also properly reproduced (e.g. 4/5 October for both 218
radars). Over the whole validation period, the normalized estimation error has a mean
219
of 0.6 and a variance of 1.3 at Herzeele radar location (n=164), and a mean of -0.8 and
220
a variance of 1.3 at Sempach radar location (n=264). These normalized estimation 221
errors indicate a tendency of the model to slightly overestimate bird densities in 222
Herzeele and to underestimate it in Sempach. Finally, both variances were close to one,
223
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which shows that the model provides a reliable uncertainty range. Overall, the 224
root-mean-square error of the non-transformed variable (i.e. the actual bird densities) 225
was around 20 bird/km2for both radars, which demonstrates the good performance of 226
the model at these two test locations. 227
0
20
40
60
80
100
120
140
Bird densities [bird/km2]
Uncertainty range
Estimate Z*
Bird radar
Sep 19 Sep 22 Sep 25 Sep 28 Oct 01 Oct 04 Oct 07 Oct 10
Date 2016
0
50
100
150
200
(a)
(b)
Figure 4.
Comparison of the estimated bird densities (black line, 10-90 quantiles uncertainty range in grey) and the
bird densities (red dots) observed using dedicated bird radars at two locations in (a) Herzeele, France (50
53’05.6”N
2
32’40.9”E) and (b) Sempach, Switzerland (47
07’41.0”N 8
11’32.5”E). Note that because of the power transformation,
model uncertainties are larger when the migration intensity is high. It is therefore critical to account for the uncertainty
ranges (light gray) when comparing the interpolation results with the bird radars observations (red dots).
Application to bird migration mapping 228
The main outcome of our model is to estimate bird densities at any time and location 229
within the domain of interest. This is illustrated by the estimation of bird densities time
230
series at specific locations (e.g. Figure 4), and by the generation of bird densities maps
231
at different time steps (Figure 5). 232
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1 10 100 15050
Daily average bird density [bird/km2]
18:00 19:00 20:00 21:00 22:00 23:00
00:00 01:00 02:00 03:00 04:00 05:00
Rain
Figure 5.
Maps of bird densities estimation every hour of a single night (4/5 October). Civil sunset and sunrise limits
are visible on the first and last snapshots. The highest bird densities are in the corridor from Northern Germany to
southwestern France. Rain limits migration in Southern Poland, Czech Republic and Southern Germany. The sunrise and
sunset fronts are visible at 18:00 and 05:00 with lower densities close to the fronts. A rain cell above Poland blocked
migration on the Eastern part of the domain. In contrast, a clear pathway is visible from Northern Germany through to
Southwestern France.
While the estimation represents the most likely value of bird density at each node of
233
the grid (e.g. Figure 5), a simulation generate several realizations (i.e. equiprobable 234
outcomes of the migration process) that reproduce the space-time patterns of migration
235
(e.g. Figure 6). As a consequence, only realizations are able to reproduce number during
236
peak migration as noted when comparing the colorscale of Figure 5 and Figure 6. This
237
becomes important when assessing for instance the total number of birds aloft. 238
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0
1
100
1000
Bird densities [bird/kmi
2]
Rain
Realization 1 Realization 2 Realization 3
Figure 6.
Snapshot of three different realizations showing peak migration (4 October 2016 21:30 UTC). The total
number of birds in the air for these realisations was 119, 126 and 120 million respectively. Comparing the similarity and
differences of bird densities patterns among the realisations illustrates the variability allowed by the stochastic model used.
The texture of these realisations is more coherent with the observations than the smooth estimation map in Figure 5.
For each of the 100 realisations, we computed the total number of birds flying over 239
the whole domain for each time step (Figure 7b). Within the time periods considered in
240
this study, the peak migration occurred in the night of 4/5 October with up to 120 241
million [10-90 quantiles: 107-134] birds flying simultaneously. Computing this on 242
sub-domains such as countries highlight the geographical differences in migration 243
intensity. For instance, on the same night, France had 44 [39-51] million birds aloft (89
244
bird/km2), 20 [15-25] million for Poland (65 bird/km2), and only 8 [7-10] million in 245
Finland (30 bird/km2) (Figure 7c). 246
0
50
100
Sep 19 Sep 22 Sep 25 Sep 28 Oct 01 Oct 04 Oct 07 Oct 10
Date 2016
0
10
20
30
40
50
Total number of bird aloft [millions]
Full domain France Poland Finland Uncertainty range
(a) (b)
(c)
Figure 7.
Averaged time series of the total number of birds in migration over the whole domain (black line), France (blue
line), Poland (yellow line) and Finland (red line) and their associated uncertainty ranges (10-90 quantiles, light grey).
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The spatio-temporal dynamics of bird migration can be visualized with an animated
247
and interactive map (available online at birdmigrationmap.vogelwarte.ch with user 248
manual provided in Supporting Information S5), produced with an open-source script 249
(github.com/Rafnuss-PostDoc/BMM-web). In the web app, users can visualize the 250
estimated maps or a single simulation maps animated in time, as well as time series of 251
bird densities of any location on the map. In addition, it is also possible to compute the
252
number of birds over a custom area and download all of these data through a dedicated
253
API. 254
Discussion 255
The model developed here can estimate bird migration intensity and its uncertainty 256
range on a high-resolution space-time grid (0.2
lat. lon. and 15 min.). The highest total
257
number of birds flying simultaneously over the study area is estimated to 120 million 258
[10-90 quantiles: 107-134], corresponding to an average density of 52 birds/km2. This 259
number illustrates the impressive magnitude of nocturnal bird migration, and resembles
260
values of peak migration estimated over the USA with 500 million birds and a similar 261
average density of 51 birds/km2(Van Doren & Horton, 2018). For more local results, 262
interactive maps of the resulting bird density are available on a website with a 263
dedicated interface that facilitates the visualisation and the export of the estimated bird
264
densities and their associated uncertainty (birdmigrationmap.vogelwarte.ch, see 265
Supporting Information S5 for a user manual). 266
Advantages and limitations 267
This paper presents the first spatio-temporal interpolation of nocturnal bird densities at
268
the continental scale that accounts for sub-daily fluctuations and provides uncertainty 269
ranges. In contrast to the methods based on covariates that are deemed more reliable 270
for extrapolation in space and time (Erni et al., 2002; Van Belle, Shamoun-Baranes, Van
271
Loon, & Bouten, 2007; Van Doren & Horton, 2018), our interpolation approach does not
272
require any external covariate per se (e.g. temperature, rain, or wind). Although local 273
features such as the approach of a rain front, the proximity to the ocean, or the 274
presence of mountains will affect bird migration, these were not explicitly accounted for
275
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in the current model. However, their influence on bird migration is partially captured 276
by the measurements of weather radars, so that, in turn, the interpolation implicitly 277
accounts for them. Yet, if such covariates are available, the model can easily be adapted
278
to incorporate information from these covariates through co-kriging (e.g. Chil`es & 279
Delfiner, 1999). However, adding these covariables to the interpolation is only 280
advantageous if the correlation between bird densities and these covariates is stronger 281
than the spatio-temporal correlation of the nearby radars. 282
In addition to quantifying bird migration at high resolution, we can also deduce the
283
spatio-temporal scales at which migration is happening from the covariance function of
284
the model (Figure S3-5 in Supporting Information S3). For instance, the amplitude of 285
bird migration correlates over distances up to 700 km and over periods of up to 5.5 days
286
(i.e. distance for which the auto-covariance has reached 10% of its baseline value, see 287
Supporting Information S3 for details). These decorrelation ranges of the amplitude 288
scale the spatio-temporal extent of broad front migration in the midst of the autumn 289
migration season and highlight the importance of international cooperation for data 290
acquisition and for spread of warning systems on peak migration events. 291
As a proof of concept, we used three weeks of bird densities data available on the 292
ENRAM data repository (see Data Accessibility). As more data from weather radars 293
become available, our analyses can be extended to year-round estimations of migration
294
intensity at the continental scale, in Europe and in North America. We also importantly
295
pre-processed the bird density data, i.e. restricted our model to nocturnal movements 296
and applied a strict manual data cleaning. This is because the bird density data 297
presently made available can be strongly contaminated with the presence of insects 298
during the day, and birds flying at low altitude are not reliably recorded by radars 299
because of ground clutter and the radar position in relation to its surrounding 300
topography. Once the quality of the bird density data has improved, our model can be
301
implemented in near-real-time and provide continuous information to the stakeholder, 302
public and private sector. 303
Although we think that the model introduced here can already be a valuable tool 304
(see below), we see several avenues for further development. For instance, in applications
305
where the distribution of flight altitudes is crucial, the model can be extended to 306
explicitly incorporate the vertical dimension. Furthermore, if fluxes of birds, i.e. 307
16/20
migration traffic rates, are sought after, a similar geostatistical approach can be used to
308
interpolate flight speeds and directions that are also derived from weather radar data. 309
Applications 310
Many applied problems rely on high-resolution estimates of bird densities and migration
311
intensities and the model developed here lays the groundwork for addressing these 312
challenges. For instance, such migration maps can identify migration hotspots, i.e. areas
313
through which many aerial migrants move, and thus, assist in prioritising conservation 314
efforts. Furthermore, mitigating collision risks of birds by turning off artificial lights of
315
tall buildings or shutting down wind energy installations requires information on when 316
and where migration intensity peaks. The probability distribution function of our model
317
can provide this as it estimates when and where migration intensity exceeds a given 318
threshold. Such information can be used in shut-down on demand protocols for wind 319
turbine operators, or trigger alarms to infrastructure managers. 320
Acknowledgements 321
This study contains modified Copernicus Climate Change Service Information 2019. Neither the European Commission 322
nor ECMWF is responsible for any use that may be made of the Copernicus Information or Data it contains. We 323
acknowledge the European Operational Program for Exchange of Weather Radar Information (EUMETNET/OPERA) 324
for providing access to European radar data, facilitated through a research-only license agreement between 325
EUMETNET/OPERA members and ENRAM (European Network for Radar surveillance of Animal Movements). 326
Mathieu Boos kindly provided the BirdScan data for Herzeele in France. We acknowledge the financial support from the
327
Globam project funded by BioDIVERSA, including the Swiss National Science Foundation (31BD30 184120), 328
Netherlands Organisation for Scientific Research (NWO E10008), Academy of Finland (aka 326315), BelSPO 329
BR/185/A1/GloBAM-BE. 330
Authors’ contributions 331
RN, LB, FL, BS conceived the study, RN, LB, GM designed the geostatistical model, RN developed and implement the
332
computational framework, RN, LB, BS performed the analyses and wrote a first draft of the manuscript, with substantial
333
contributions from all authors. 334
17/20
Data Accessibility 335
The Github page of the project (rafnuss-postdoc.github.io/BMM contains the MATLAB livescript for the 336
interpolation rafnuss-postdoc.github.io/BMM/2016/html/Density inference cross validation.html) and 337
the creation of the figures (rafnuss-postdoc.github.io/BMM/2016/html/paper figure). 338
Raw weather radar data are available on the ENRAM repository (github.com/enram/data-repository). 339
The cleaned vertical time series profile are available on Zenodo (
doi.org/10.5281/zenodo.3243397
) (Nussbaumer,
340
Benoit, Mariethoz, et al., 2019) 341
The final interpolated maps are available on Zenodo (
doi.org/10.5281/zenodo.3243466
) (Nussbaumer, Benoit, &
342
Schmid, 2019). 343
The code of the website (HTML, Js, NodeJs, Css) are available on the Github page 344
(github.com/rafnuss-postdoc/BMM-web)345
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Supporting Information 346
S1 Data pre-processing 347
Supporting Information S1 describes the full procedure applied to manually clean the raw time series of bird densities. 348
The raw dataset have been previously published in (Nilsson et al., 2019) and is available on the ENRAM data repository
349
(
github.com/enram/data-repository
). The steps detailed below are illustrated in Figure S1-1 for the radar located in
350
Zaventem, Belgium (5054’19”N, 427’28”E). 351
1.
The data of 11 radars are discarded because their quality was deemed insufficient by visual inspection. The reasons
352
for this poor quality are various: S-band radar type, altitude cut, poor processing or large gaps. The same radars 353
were removed in (Nilsson et al., 2019). In addition, we also excluded radars of Bulgaria and Portugal (4 radars) from
354
this study because of their geographic isolation and the necessity of spatial coherence in the methodology presented.
355
2. If rain is present at any altitude bin, the full vertical profile was discarded (blue rectangle in Figure S1-1). A 356
dedicated MATLAB GUI was used to visualise the data and manually set bird densities to “not-a-number” in such
357
cases. 358
3.
Zones of high bird densities are sometimes incorrectly eliminated in the raw data (red rectangle in Figure S1-1). To
359
address this, (Nilsson et al., 2019) excluded problematic time or height ranges from the data. Here, in order to keep
360
as much data as possible, the data have been manually edited to replace erroneous data either with “not-a-number”,
361
or by cubic interpolation using the dedicated MATLAB GUI. 362
4.
Due to ground scattering, the lowest altitude layers are sometimes contaminated by errors, or excluded by the initial
363
automatic cleaning procedure. This is solved by copying the first layer without error into to the lowest ones. 364
5.
The vertical profiles are vertically integrated from the radar altitude (brown line in Figure S1-1c) and up to 5000 m
365
a.s.l. 366
6.
Finally, the data recorded during daytime are excluded. Daytime is defined at each radar by the civil dawn and dusk
367
(sun 6below horizon). 368
The resulting cleaned vertical-integrated time series of nocturnal bird densities are displayed in Figure S1-1d. 369
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Figure S1-1.
Example of the cleaning procedure from raw reflectivity to areal bird densities for the radar of Zaventem,
Belgium (50
54’19”N, 4
27’28”E). (a) raw reflectivity measurements; (b) Automatically cleaned vertical bird profiles; (c)
Manually cleaned vertical bird profiles; (d) Final bird densities (integrated over altitudes).
S2 Details on the geostatistical model 370
Supporting Information S2 expends the explanation given in the section Geostatistical model. In particular, it provides 371
the mathematical development for the kriging equations of the amplitude and residual as well as the reconstruction of the
372
bird densities estimation. 373
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Standardization 374
For the convenience of the kriging equation, we introduce the standardized (i.e. normal transformed) variable
˜
A
(
s, t
) and
375
˜
R
(
s, t
) of the amplitude and residual respectively. Because the trend removed the average of the amplitude (i.e.
E
(
A
) = 0
376
), the standardized amplitude is 377
˜
A(s, t) = A(s, t)
σA
,(S2-1)
where σA=pvar (A) is the empirical standard deviation of A. The standardized residual is 378
˜
R(s, t) = R(s, t)
σR(s, t),(S2-2)
where the variance σR(s, t) is modelled by a polynomial function of the local NNT because of the strong correlation of 379
the variance of the residual with the NNT ( Figure S3-3 in Supporting Information S3), 380
σR(s, t) =
i=6
X
i=0
biNNT(s, t)i,(S2-3)
where biare the coefficients of the polynomial. 381
Covariance function 382
Both the amplitude and the residual are modelled as stationary processes which can be described with a covariance
function (also called auto-covariance). Let us denote the generic standardized random variable ˜
Xfor either the
standardized amplitude ˜
Aor the standardized residual ˜
R. The covariance C˜
Xis a positive definite function depending
only on the lag-distance (∆s,t). In our model, we use covariance functions of Gneiting type (Gneiting, 2002)
C˜
X(∆s,t) = cov ˜
X(s,t),˜
X (s+ ∆s,t + ∆t)
=C0+1
(∆t/rt)2δ+ 1 exp
(ksk2/rs)2γ
(∆t/rt)2δ+ 1βγ
.
(S2-4)
In this model, rtand rsare the scale parameters (in space and time respectively). They control the decorrelation 383
distances and thus, the average extent and duration of the space-time patterns of ˜
X. 0 < δ,γ < 1 are regularity 384
parameters (in space and time respectively) and control the shape of the covariance function close to the origin. Values of
385
δand γclose to 0 lead to sharp variations at short lags, while values close to 1 lead to smooth variations of ˜
A. The 386
separability parameter βcontrols the space-time interactions. When β= 0 the space-time interactions vanish and the 387
covariance function becomes space-time separable. Finally, C0is the nugget, which accounts for the uncorrelated 388
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variability of the process at hand. 389
Kriging 390
Both the standardized amplitude and residual can be estimated by kriging as explained below (Figure S2-1). Kriging 391
provides an estimated value of the random variable
˜
X
(
s0, t0
)
at the target point (
s0, t0
) based on a linear combination of
392
observations at the n0closest space-time locations ˜
X(sα, tα)with 393
˜
X(s0, t0)=
α=n0
X
α=1
λα˜
X(sα, tα).(S2-5)
The kriging weights Λ= [λ1,· · · , λn0]Tare derived from the covariance function of the random process ˜
X. More 394
precisely, the kriging weights are the solution of the following linear system, commonly referred to as the kriging system,
395
Cα,αΛ=Cα,0,(S2-6)
with
Cα,α
the covariance matrix between observations and
Cα,0
the covariance matrix between the observations and the
396
target point. These covariances are computed using the fitted covariance function of Eqn. S2-4 397
Cα,0=C˜
X(sαs0, tαt0).(S2-7)
The kriging weights can be solved using Λ=C1
α,αCα,0, and used in Eqn. S2-5 to compute the kriging estimate. 398
4/20
28-Sep
29-Sep
55
Time
30-Sep
20
50
Latitude 15
Longitude
10
45 5
0
-14
-10
-6
-2
Kriging Weight Value (log-scale)
Figure S2-1.
Illustration of the kriging weights computed for an estimation performed at the red dot location. Here we
illustrate only the neighbours whithin +/- 1 day and a spatial neighbourhood of 600 km.
In addition to the estimated value
˜
X(s0, t0)
, kriging also provides a measure of uncertainty with the variance of the
399
estimation, 400
var ˜
X (s0,t0)= C˜
X(0,0) ΛtCα,0(S2-8)
Reconstruction of the transformed bird densities 401
The transformed variable Z(s0, t0)pis reconstructed by combining the deterministic parts (trend and curve) with the
kriging estimation of the amplitude and residual as in Eqn. 1. Because Aand Rare normally distributed, Zpis also
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normally distributed and its mean µp
Zand variance σ2
Zpare sufficient to describe its distribution with
µZp=E(Z(s0, t0)p)
=E(t(s0) + A(s0, t0) + c(t0) + R(s0, t0))
=t(s0) + E(A(s0, t0)) + c(t0) + E(R(s0, t0))
=t(s0) + ˜
A(s0, t0)σA+c(t0) + ˜
R(s0, t0)σR(s0, t0)
(S2-9)
and as Aand Rare independent,
σ2
Zp= var (A(s0, t0) + R(s0, t0))
= var (A(s0, t0)) + var (R(s0, t0))
= (σ˜
A(s0, t0)σA)2+ (σ˜
R(s0, t0)σR(s0, t0))2.
(S2-10)
S2.1 Probability distribution function of bird densities 402
Because of the power-transform, the probability distribution function (pdf) of Z, denoted by fZ(z), is non-trivial. 403
However, the quantiles of this pdf can be derived analytically from the quantiles of the pdf of Zpas detailed hereafter. 404
We introduce the normally distributed variable X=Zpwith a pdf 405
fX(x) = 1
p2σ2
Zpπexp (xµZp)2
2σ2
Zp!,(S2-11)
where µZpand σ2
Zpare the mean and variance of Zpderived from Eqn. S2-9 and S2-10. 406
One possible way to compute the pdf of Zpconsists in computing the mean of several functions of this random 407
variable. For any given measurable function g,408
EgX1/p =
Z
−∞
gx1/p fx(x) dx. (S2-12)
Using the change of variable z=x1/p , which leads to dx=pZp1dz, Eqn. S2-12 becomes 409
E(g(Z)) =
Z
−∞
g(z)pZp1fX(Zp) dz. (S2-13)
6/20
This equation allows identifying the pdf of Zas 410
fZ(z) = pZp1fX(x).(S2-14)
This last equation provides the analytical pdf of bird densities Z, as the pdf fX(x) = fZp(zp) is fully known 411
Zp∼ N µZp, σ2
Zp.412
Quantile function 413
The probability distribution function of
Z
is non-symmetric and skewed, and therefore cannot be conveniently described
414
with this expected value and variance. Instead, we use the quantile function
QZ(ρ;s0, t0)
, which returns the bird density
415
value zcorresponding to a given quantile ρ416
QZ(ρ;s0, t0) = z|Pr (Z(s0, t0)< z) = ρ. (S2-15)
The quantile function allows to describe Zbecause the quantile value ρis preserved through power transform. 417
Therefore, the quantile function of Zis computed with 418
QZ(ρ;s0, t0) = QZp(ρ;s0, t0)1/p =F1
Zp(ρ)1/p ,(S2-16)
where FZp(Zp) is the cumulative distribution function of Zp(s0, t0). 419
S3 Model parametrisation 420
Supporting Information S3 presents the method of parametrisation and discusses the meaning of model parameters in 421
terms of bird migration. 422
Power transform 423
The value of power transformation pis inferred by maximizing the Kolmogorov-Smirnov criterion of the p-transformed 424
observation data Z(s, t)p. The Kolmogorov-Smirnov test (Massey, 1951) is testing the hypothesis that data Z(s, t)pare 425
normally distributed. The optimal power transformation parameter was found for p= 1/7.4 and the resulting Zp426
histogram is illustrated in Figure S3-1 together with the initial data Z.427
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Figure S3-1.
Histogram of the raw bird densities data
Z
(top) and the power transformed bird densities
Zp
(bottom)
for the calibrated parameter p= 1/7.4.
The fitted distribution shows that bird densities is highly skewed: the lowest 10% are below 1 bird/km2while the 428
upper 10% are above 50 bird/km
2
with density up to 500 bird/km
2
. A power transformation on such skewed data creates
429
significant non-linear effects in the back-transformation. For instance, the symmetric uncertainty of an estimated value in
430
the transformed space (quantified by the variance of estimation) will become highly skewed in the original space. 431
Consequently, the uncertainty of the estimation of bird densities is highly dependent on the value of the power transform:
432
low densities estimations have a smaller uncertainty than high densities. This motivates the importance of providing the
433
full distribution of the estimation. Indeed, the traditional central value (mean of 19 bird/km
2
and median of 8 bird/km
2
)
434
would be unable to capture the distribution adequately. Such effects also have consequences from an 435
ecological/conservation point of view. Indeed, efficient protection of birds along the migration route (from artificial light
436
or wind turbines) need to pay particular attention to the peak densities, where the majority of birds are moving in a few
437
nights. These peaks can only be successfully reproduced by taking care of the high tail of the distribution. This is done
438
here by using a full distribution for the estimation. 439
Trend and curve 440
The parameters of the deterministic components of the model (i.e. trend and curve) are calibrated based on the 441
transformed data measured at the radar locations. This step involves the calibration of 3 parameters for the trend 442
(wlat, wlon , w0), 6 for the curve (ai) and also the values of the amplitude for each radar and for each night (i.e. 443
nradar ·nday values). The calibration is performed by minimizing the misfit function between the modeled and the 444
observed data. In practice, a local search algorithm is used (fminsearch function of MATLAB which uses a simplex 445
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algorithm). This local search algorithm requires initial values for each parameter, which are computed sequentially: (1) 446
the initial trend is fitted to the average of the transformed bird densities for each radar, (2) the amplitudes are computed
447
from the de-trended data, and (3) the parameters of the curve are derived by fitting a polynomial on the data corrected
448
from the trend and amplitude effects. After convergence of the algorithm, the resulting misfit value becomes the value of
449
the residual. The resulting planar trend is shown in Figure S3-2a together with the average transformed bird densities of
450
each radar. The trend displays a strong North-South gradient, which can be explained by the larger migration activity in
451
southern Europe during the study period. A 2-dimensional planar trend was initially tested in order to accommodate the
452
northeast-southwest flyway. However, this more complex model did not significantly improved the fit to data, and has 453
therefore been discarded. The de-trended values illustrated in Figure S3-2b are more stationary with the exception of 454
Finland and Sweden. (Nilsson et al., 2019) also noted this difference between both countries, but excluded the fact that
455
this difference is due to errors in the data since the southern Swedish radar shows consistent amounts of migratory 456
movements with a neighbouring German site. Figure S3-2b highlights the central European continental flyway as 457
illustrated by the arrow. 458
Transformed bird densities
-0.3
-0.2
-0.1
0
0.1
0.2
1
1.2
1.4
1.6
Transformed bird densities
Figure S3-2. (left) Fitted trend with corresponding observation at radar location and (right) detrended data.
Figure S3-3 displays the fitted curve (black line) together with the calibration data. The curve reveals that the 459
migration is mainly concentrated between 10-90% of the nighttime with larger densities of birds in the first half of the 460
night. A slight asymmetry with steeper rise at the beginning of the night and smoother transition with the day is also 461
visible. The larger variance of the data around the calibrated curve at the beginning and end of night is due to the 462
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power-transformation of the raw data and accounted for in the model. However, the large variance of the data used to 463
adjust the curve model shows a significant intra-night variability in bird migration. This highlights the importance of 464
modelling the intra-night fluctuations by the residual term and stresses the limitation of using nightly averages or single
465
point observations (e.g. 3hr after sunset) if high precision estimates are required. 466
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Normalized Night Time (NNT)
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Transformed bird densities
Figure S3-3.
Individual observations (black dots) and adjusted model (black line) of the nightly curve. Shaded grey
areas denote 1-, 2- and 3- sigma uncertainty ranges.
As no clear spatial patterns appear in the curve parameters, a single curve model is used for the entire study domain.
467
The suitability of this unique curve model is validated by the spatially-uncorrelated mean and variance of the residual 468
signal displayed in Figure S3-4. 469
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-0.2
-0.1
0
0.1
0.2
0.5
1
1.5
(a) (b)
Figure S3-4. (a) Mean and (b) standard deviation of residual value for each radars.
Amplitude and residual 470
The parameters of the space-time covariance function (n, rt, rs, δ, γ, β) of the amplitude and residual are inferred from 471
empirical covariances derived for several lag-distances and lag-times on an irregular grid. Then, the parameters of the 472
Gneiting covariance function are inferred by minimizing the root mean square error between empirical and modelled 473
covariances. Both covariance functions of the amplitude and residual are best fitted with a separable model (β= 0), 474
meaning that they can be fully described by the product of a spatial covariance function (Figure S3-5a and c) and a 475
temporal covariance function (Figure S3-5 b and d). 476
Covariance function of the amplitude and residual 477
The calibrated covariance functions provide information about the degree of spatial and temporal correlation of the bird
478
migration process. The spatial covariance of the amplitude (Figure S3-5a) shows that the nocturnal bird densities are 479
well-correlated for locations separated by less than 500 km, and completely uncorrelated for more than 1500 km. The 480
temporal covariance has an asymptotic behavior and never decreases under 0.2 (Figure S3-5b). This non-zero sill can be
481
due to either a remaining temporal non-stationarity in the dataset, or systematic errors in radar observations (caused by
482
e.g. different types of technology or local topography affecting migration). Note that since the covariance is evaluated 483
only on a discrete 1-day lag-distance, the shape of the covariance between 0 and 1 is artificially created to fit the Gneiting
484
function. Overall, the temporal correlation of the amplitude is weak with only 40% for the covariance for lag-1. It is 485
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Table 1. Calibrated parameters
Power Transformation p= 0.135
Trend w0= 2.62 , wlat =0.024
Covariance of amplitude nugget/sill = 0%, β= 0, rt= 0.39, rs= 174, δ= 0.18,
γ= 0.43
Curve a= [0.720.120.76 0.05 0.29 0.070.05]
Curve variance b= [0.010.030.00 0.010.000.00]
Covariance of residual nugget/sill = 7.7%, β= 0, rt= 0.048, rs= 206, δ= 1,
γ= 0.47
important to recall that since the weather radars are relatively well-spread (Figure 1b), the spatial covariance of both the
486
amplitude and residual is poorly constrained for lag-distances below 100 km, and consequently the importance of the 487
nugget (Eqn. S2-4) is unknown. The temporal correlation of the residual is very high for short lags (
<
2 hr) and indicates
488
consistent measurements of each weather radars. The small covariance value for larger lag-distances demonstrates that 489
the curve account for most of the stationary component at this scale. 490
0 500 1000 1500 2000
0
0.5
1
0246810
0 200 400 600 800 1000
Distance [km]
0
1
Covariance
0 0.1 0.2 0.3 0.4
Time [Days]
(b)(a)
(c) (d)
Residual Amplitude
0.5
Figure S3-5. Illustration of the calibrated covariance function of (a-b) amplitude and (c-d) residual.
The table below summarizes the fitted parameters. 491
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S4 Cross-validation 492
Supporting Information S4 extends the results of the Cross-validation section. First of all, Figure S4-1 displays the 493
histogram of the normalized errors of kriging (Eqn. 5) when all data across all radars are combined. The mean of the 494
distribution is close to zero which indicates that the estimation is unbiased (i.e. in average, the estimation is neither 495
underestimating (mean below 1) nor overestimating (mean above 1)). However, its variance is below 1, which indicates a
496
slight overestimation of the uncertainty range (i.e. in average, the uncertainty ranges are too wide). 497
-4 -3 -2 -1 0 1 2 3 4
0
0.1
0.2
0.3
0.4
0.5
0.6
Normalized error of kriging with mean: -0.017 and variance: 0.61
Figure S4-1.
Histogram of the normalized error of kriging for all radars combined. The red curve is the standard normal
distribution which should be matched by the histogram.
Next, the normalized kriging error is assessed for each radar (Figure S4-2). The resulting distributions indicate that 498
the goodness of the estimation is different for each radar. In Figure S4-3, their means and standard deviations do not 499
reveal any spatial pattern, thus suggesting no spatial biases. 500
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bejab
bewid
bezav
czbrd
czska
deboo
dedrs
deeis
deess
defbg
defld
dehnr
deisn
demem
deneu
denhb
deoft
depro
deros
detur
deumd
fianj
fiika
fikes
fikor
fikuo
filuo
fipet
fiuta
fivan
fivim
frabb
frave
frbla
frbor
frbou
frcae
frche
frgre
frlep
frmcl
frmom
frmtc
frniz
frpla
frtou
frtra
frtre
frtro
nldbl
nldhl
plbrz
plgda
plleg
plpoz
plram
plrze
plswi
seang
searl
sease
sehud
sekir
sekkr
selek
selul
seovi
sevar
sevil
-4
-3
-2
-1
0
1
2
3
4
Normalized error of kriging
Figure S4-2.
Boxplot of the normalized kriging error for each radar. A negative (positive) value indicates an
underestimation (overestimation) of the method. The cross-validation for the Czech (czbrd, czska) and Swedish radars
(se***) shows a constant underestimation (except for selul). Overall, the goodness of the estimation is variable and
radar-dependent.
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0.5
-1
-1.5
0.5
0
1
1.5
1
1.5
0.5
Mean
Variance
Figure S4-3.
Mapping of the mean and variance of the normalized error of kriging for each radar. The reproduction of
the variance is illustrated by a black circle, for which a perfect variance would match the colour circle and a smaller circle
indicates an under-confidence (uncertainty range too large).
The cross-validation is further illustrated in Figure S4-4 for a specific radar located in Boostedt, Germany 501
(54
00’16”N, 10
02’49”E) indicated with gold circle in Figure S4-3. For this radar, the general pattern of the signal is well
502
estimated for both the nightly amplitude and the intra-night variation. Bird densities are underestimated during the peak
503
migration occurring at 4th and 5th of October, is but the estimated value remains within the uncertainty bounds. 504
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25-Sep 02-Oct 09-Oct
Date
0
50
100
150
200
250
Bird densities [bird/km
2]
Uncertainty range
Estimate Z*
Weather radar data
Figure S4-4.
Comparison of bird densities estimated with the model in a cross-validation setup and observed by the
weather radar for the radar located in Boostedt, Germany (54
00’16”N, 10
02’49”E). The uncertainty range is defined as
the 10 and 90 quantiles.
S5 Manual for website interface 505
The following Supporting Information describes the web interface developed for visualization and querying of the 506
interpolated data. The website is available at birdmigrationmap.vogelwarte.ch and the code at 507
github.com/Rafnuss-PostDoc/BMM-web. Figure S5-1 displays the web interface along with the possible interactions, 508
which are further detailed below. 509
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Figure S5-1. Website interface with identification key for the interactive components of each block
Block 1: interactive map 510
The main block of the website is a map with a standard interactive visualization allowing for zoom and pan. On top of 511
this map, three layers can be displayed: 512
Layer 1 corresponds to bird densities displayed in a log-color scale. This layer can display either the estimation map,
513
or a single simulation map by using the drop-down menu (1a). 514
Layer 2 corresponds to the rain (rainy areas are in light blue), which can be hidden/displayed with a checkbox (1b)
515
Layer 3 corresponds to the bird flight speed and direction, displayed by black arrows. The checkbox allows to 516
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display/hide this layer (1c). The last item on the top-right menu is the link menu (1d). 517
Block 2: time series 518
The second block (hidden by default on the website) shows three time series, each in a different tab (2a): 519
Densities profile shows the bird densities [bird/km2] at a specific location. 520
Sum profile shows the total number of bird [bird] over an area. 521
MRT profile shows the mean traffic rate (MTR) [bird/km/hr] perpendicular to a transect. 522
A dotted vertical line (2d) appears on each time series to show the current time frame displayed in the map. Basic 523
interactive tools for time series include zooming on a specific time period (day, week or all period) (2b) and general zoom
524
and auto-scale (2e). Each time series can be hidden and displayed by clicking on its legend (2c). The main feature of this
525
block is the ability to visualise bird densities time series for any location chosen on the map. For the densities profile tab,
526
the button with a marker icon (2f) lets you plot a marker on the map, and displays the bird densities profile with 527
uncertainty (quantile 10 and 90) on the time series corresponding to this location. You can plot several markers to 528
compare the different locations (Figure S5-2). Similarly, for the sum profile, the button with a polygon icon (2f) lets you
529
draw any polygon and returns the time series of the total number of birds flying over this area. For the MTR tab, the 530
flux of birds is computed on a segment (line of two points) by multiplying along the segment the bird densities with the
531
local flight speed perpendicular to that segment. 532
Block 3: time control 533
The third block shows the time progression of the animated map with a draggable slider (3d). You can control the time
534
with the buttons play/pause (3b), previous (3a) and next frame (3c). The speed of animation can be changed with a 535
slider (3e). 536
API 537
An API based on mangodb and NodeJS is available to download any of the time series described in Block 2. Instructions
538
can be found at github.com/Rafnuss-PostDoc/BMM-web#how-to-use-the-api 539
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Examples 540
Figure S5-2.
Print-screen of the web interface developed to visualize the dataset. The map shows the estimated bird
densities for the 23rd of September 2016 at 21:30 with the rain mask appearing in light blue on top. The domain extent is
illustrated by a black box. The time series in the bottom shows the bird densities with quantile 10 and 90 at the two
locations symbolized by the markers with corresponding color on the map. The button with a marker symbol on the right
side of the time series allows to query any location on the map, and to display the corresponding time series.
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Figure S5-3.
Print-screen of the web interface with the simulation map for the 3rd of October at 23:00. The bottom
panel shows the time series of the total number of birds corresponding to the polygon drawn over the map according to
their colour. The button with the polygon symbol on the right side of the time series allows to query the total number of
birds flying any polygon drawn on the map.
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Observation of animals flying in the atmosphere is the core empirical process of aeroecology. For species that are small, or that fly by night or at high altitudes, this presents a considerable challenge. Even for the more visible species and for flights near the ground, recording the animals’ movements requires specialised techniques. Fortunately, continuing rapid advances in radio and optical technologies, electronics, and computing are providing numerous opportunities for developing new and improved observing capabilities. The larger, more complete, and more precise observational datasets that these new technologies are providing underlie the current wave of discovery and growth in this novel discipline. This chapter is mainly concerned with methods for detecting and studying insects, birds, and bats flying in the open air, i.e. above the vegetation layer. Detection of these animals, and estimation of their numbers, can be achieved through in-flight capture or by remote sensing, with the latter comprising visual observation (including technologies for augmenting human sight), aural monitoring, radar, and laser/lidar. Remotely sensed animals can be identified, though sometimes only to a group of species, from characteristic features of the signals or images received. Information about the animals’ activities—their mode of flight, orientation, etc.—can be obtained either by remote sensing or from sensors mounted on the animals. The latter method, which relies on radio-telemetry or archival logging to record the acquired data, may also be used to monitor the animal’s physiological state, the environment it is moving in, and its trajectory. The chapter also examines how information about the timing and geographical extent of movements, and the environmental conditions the animals are experiencing, can be obtained. Finally, the particular challenges of observational aeroecology are identified, the multidisciplinary nature of the observing task is recognised, and some possible developments are proposed.